1. Routing and Scheduling in Multistage Networks using Genetic Algorithms Advisor: Dr. Yi Pan Chunyan Ji 3/26/01

2. Presentation Outline Background and Motivation of this research Genetic Algorithm Analysis of Testing Results Simulation Package in Java Applet Conclusion and Future work Demo

3. Background and Motivation of this research Multistage Interconnection Network Network size N=2 n (n is the number of stages) N/2 switching elements in each stage

4. Crosstalk in OMIN Two ways to produce undesired coupling in a Switching Element

5. Approaches to avoid crosstalk 2N*2N regular OMIN to provide N*N connection Routing traffic through an N*N OMIN to avoid coupling two signals within each Switching Element

6. Legal path in SW at a time Paths without crosstalk in SE:

7. Omega Network Each connection between stages is shuffle-exchanged 000->000 001->010 010->100 … 111->111

8. Routing in Omega Network

9. Routing same ex. in 2 passes

11. The Window Method

12. Conflict Graph

13. Routing Algorithm While (not end of messages list) 1. Select one of the left messages; 2. Schedule the message in a time slot with no conflict with other messages that have been already scheduled.

14. Four Routing Algorithms Sequential Algorithm: Choose a message in increasing order of the message source address. Seq-Down Algorithm: Choose a message in decreasing order of the message source address. Degree-ascending Algo: Choose a message in the order of the increasing degrees in conflict graph. Degree-descending Algo: Choose a message in the order of the decreasing degrees in conflict graph

15. Genetic Algorithm

16. Chromosomes Binary: 01011010 Permutation encoding:21314231 Index represents the node in the graph and the integer value represents the color of its corresponding node

17. Operators of GA Crossover Mutation Selection

18. Crossover Single Crossover: Parent 1: 2311242212341 Parent 2: 1232422311243 After crossover, Offspring 1: 2311242311243 Offspring 2: 1232422212341

19. Operators of GA(cont.) Double Crossover Parent 1: 2311242212341 Parent 2: 1232422311243 After double crossover, Offspring 1: 2312422312341 Offspring 2: 1231242211243

20. Mutation Offspring from the crossover: Offspring 1 : 2311242311243 Offspring 2 : 1232422212341 Offspring after mutation: Offspring 1 : 2312242311243 Offspring 2 : 1232322212311

21. Selection Fitness Function:number of colors valid solutions Betting fitting offspring (less number of colors) gets to be the parent of next generation

22. Parameters of GA Crossover Probability Mutation Probability Population Size Number of Generations

23. Example

24. Sequential Algo. Coloring

25. Degree-descending Coloring

26. GA Coloring(MP=0.1,Gen=100)

27. Analysis of testing results

28. Color-exchanging Mutation results

29. Generations affects GA

30. Generations(MP=0.1)

31. Generations(MP=0.01)

32. Generations(MP=0.3)

33. Generations(MP=0.4)

34. Generations(MP=0.001)

35. Analysis Best Mutation Probability: 0.1---0.3 Generations:100---300 Population size:4--8 Crossover Probability used: 100% In this research, maximum colors reduced by GA: 2

36. Maximum passes reduced by GA in this research

37. Single vs. Double Crossover

38. Comparisons of 5 algorithms

39. Java Applet

40. Sequential Algo.(128*128)

41. Sequential Down Algo.

42. Degree-ascending Algo.

43. Degree-descending Algo.

44. Genetic Algorithm

45. Comparisons of 5 algorithms

46. Conclusion and Future work Genetic Algorithm can be used as a optimizing tool Disadvantage:time consuming Perform GA in parallel Other complicated GA techniques to improve the results